Z-Score Calculator
Calculate the z-score (standard score) for a data point, and estimate its approximate percentile in a normal distribution.
Results
What is it?
A z-score (or standard score) tells you how many standard deviations a particular value is from the population mean. z = (x − μ) / σ. A z-score of 0 means the value is exactly the mean; z = +1 means one standard deviation above the mean; z = −2 means two below.
How to use
Enter the data point x, the population mean μ, and the standard deviation σ. The z-score is calculated instantly. The percentile estimate uses a piecewise approximation of the standard normal CDF (Φ), telling you approximately what proportion of the population falls below your data point.
Example scenario
A student scores 75 on a test where the class mean is 70 and σ = 10. z = (75 − 70) / 10 = 0.5. This places the student at approximately the 69th percentile — they scored higher than about 69% of the class.
Pro tip
Z-scores are used in finance to detect outliers (e.g., Altman Z-Score for bankruptcy prediction), in manufacturing for quality control, and in academic testing to normalise scores across different exam versions. For precise percentiles, use a standard normal table (z-table) or the NORM.S.DIST function in Excel.